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Phenomenology of the interest curve

Author

Listed:
  • Jean-Philippe BOUCHAUD

    (Centre d'Etudes de Saclay, France)

  • Rama CONT

    (Centre d'Etudes de Saclay, France)

  • Nicole EL KAROUI

    (Ecole Polytechnique)

  • Marc POTTERS

    (Science & Finance)

  • Nicolas SAGNA

    (Credit Suisse First Boston)

Abstract

This paper contains a statistical description of the whole U.S. forward rate curve (FRC), based on data from the period 1990-1996. We find that the average deviation of the FRC from the spot rate grows as the square- root of the maturity, with a proportionality constant which is comparable to the spot rate volatility. This suggests that forward rate market prices include a risk premium, comparable to the probable changes of the spot rate between now and maturity, which can be understood as a `Value-at-Risk' type of pricing. The instantaneous FRC however departs from a simple square-root law. The distortion is maximum around one year, and reflects the market anticipation of a local trend on the spot rate. This anticipated trend is shown to be calibrated on the past behaviour of the spot itself. We show that this is consistent with the volatility `hump' around one year found by several authors (and which we confirm). Finally, the number of independent components needed to interpret most of the FRC fluctuations is found to be small. We rationalize this by showing that the dynamical evolution of the FRC contains a stabilizing second derivative (line tension) term, which tends to suppress short scale distortions of the FRC, suggesting an analogy with the motion of a vibrating string. This shape dependent term could lead, in principle, to arbitrage. However, this arbitrage cannot be implemented in practice because of transaction costs. We suggest that the presence of transaction costs (or other market `imperfections') is crucial for model building, for a much wider class of models becomes eligible to represent reality.

Suggested Citation

  • Jean-Philippe BOUCHAUD & Rama CONT & Nicole EL KAROUI & Marc POTTERS & Nicolas SAGNA, 1997. "Phenomenology of the interest curve," Finance 9712009, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpfi:9712009
    Note: Type of Document - Tex; prepared on UNIX Sparc TeX; to print on PostScript; pages: 34 ; figures: included
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    Yield curve; arbitrage; forward rate; risk premium; interest rate; volatility.;
    All these keywords.

    JEL classification:

    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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